Study of the e(g) orbitals in the bilayer manganite La(2--2x)Sr(1+2x)Mn(2)O(7) by using magnetic Compton-profile measurement.

From the magnetic Compton-profile (MCP) measurement, we have directly differentiated for the first time the populations in two e(g)-type orbitals ( x(2) - y(2) and 3z(2) - r(2)) in a manganite. The experimental MCP's along the [001] direction for La(2--2x)Sr(1+2x)Mn(2)O(7) at x = 0.35 and 0.42 are fitted by the theoretical profiles obtained from the (MnO(6))(8-) ab initio calculations. The calculation confirms that the MCP clearly detects the oxygen hybridization in the e(g) orbitals. The e(g) state is dominated by the x(2) - y(2)-type orbital with almost constant population, while the population in the 3z(2) - r(2)-type orbital decreases with increasing the hole concentration x.